Events

Abstract: In this talk, we consider a linear algebraic object known as a tridiagonal pair which arises naturally in the context of Q-polynomial distance-regular graphs. We will focus on a special class of tridiagonal pairs said to have Racah type. Given a tridiagonal pair of Racah type, we associate with it several linear transformations which act on the underlying vector space in an attractive manner and discuss their relationships with one another. In an earlier work, we introduced the double lowering operator Ψ for a tridiagonal pair. In this talk, we will explore this double lowering map further under the assumption that our tridiagonal pair has Racah type and will use the double lowering map to obtain new relations involving the operators associated with two oriented versions of our tridiagonal pair.

Abstract: We give an overview of a new Legendre-based signature scheme called Loquat that is friendly for SNARK-based applications. While we primarily focus on the constructive applications, we also discuss the historical context, security and cryptanalysis of the Legendre PRF. The primary content of the talk is based on ia.cr/2024/868.